Pressures in the Body

Typical Pressures in Humans Blood pressures in large arteries resting Blood pressure in large veins 4–15 Brain and spinal fluid lying down 5–12 Bladder Chest cavity between lungs and rib

Pressures in the Body

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Pressure in the Body

Next to taking a person’s temperature and weight, measuring blood pressure is the most common of all medical examinations Control of high blood pressure is largely responsible for the significant decreases in heart attack and stroke fatalities achieved in the last three decades The pressures in various parts of the body can be measured and often provide valuable medical indicators In this section, we consider a few examples together with some of the physics that accompanies them

[link]lists some of the measured pressures in mm Hg, the units most commonly quoted

Typical Pressures in Humans

Blood pressures in large arteries (resting)

Blood pressure in large veins 4–15

Brain and spinal fluid (lying down) 5–12

Bladder

Chest cavity between lungs and ribs −8 to −4

Digestive tract

Body system Gauge pressure in mm Hg

Blood Pressure

Common arterial blood pressure measurements typically produce values of 120 mm

Hg and 80 mm Hg, respectively, for systolic and diastolic pressures Both pressures have health implications When systolic pressure is chronically high, the risk of stroke and heart attack is increased If, however, it is too low, fainting is a problem Systolic pressure increases dramatically during exercise to increase blood flow and returns to normal afterward This change produces no ill effects and, in fact, may be beneficial

to the tone of the circulatory system Diastolic pressure can be an indicator of fluid balance When low, it may indicate that a person is hemorrhaging internally and needs

a transfusion Conversely, high diastolic pressure indicates a ballooning of the blood vessels, which may be due to the transfusion of too much fluid into the circulatory system High diastolic pressure is also an indication that blood vessels are not dilating properly to pass blood through This can seriously strain the heart in its attempt to pump blood

Blood leaves the heart at about 120 mm Hg but its pressure continues to decrease (to almost 0) as it goes from the aorta to smaller arteries to small veins (see [link]) The pressure differences in the circulation system are caused by blood flow through the system as well as the position of the person For a person standing up, the pressure in

the feet will be larger than at the heart due to the weight of the blood (P = hρg) If we

assume that the distance between the heart and the feet of a person in an upright position

is 1.4 m, then the increase in pressure in the feet relative to that in the heart (for a static column of blood) is given by

ΔP = Δhρg =(1.4 m) (1050 kg/m3)(9.80 m/s2) = 1.4 × 104 Pa=108 mm Hg

Increase in Pressure in the Feet of a Person

ΔP = Δhρg =(1.4 m) (1050 kg/m3)(9.80 m/s2) = 1.4 × 104 Pa=108 mm Hg

Standing a long time can lead to an accumulation of blood in the legs and swelling This

is the reason why soldiers who are required to stand still for long periods of time have been known to faint Elastic bandages around the calf can help prevent this accumulation and can also help provide increased pressure to enable the veins to send blood back up to the heart For similar reasons, doctors recommend tight stockings for long-haul flights

Blood pressure may also be measured in the major veins, the heart chambers, arteries to the brain, and the lungs But these pressures are usually only monitored during surgery

or for patients in intensive care since the measurements are invasive To obtain these pressure measurements, qualified health care workers thread thin tubes, called catheters, into appropriate locations to transmit pressures to external measuring devices

The heart consists of two pumps—the right side forcing blood through the lungs and the left causing blood to flow through the rest of the body ([link]) Right-heart failure, for example, results in a rise in the pressure in the vena cavae and a drop in pressure in the arteries to the lungs Left-heart failure results in a rise in the pressure entering the left side of the heart and a drop in aortal pressure Implications of these and other pressures

on flow in the circulatory system will be discussed in more detail inFluid Dynamics and Its Biological and Medical Applications

Two Pumps of the Heart

The heart consists of two pumps—the right side forcing blood through the lungs and the left causing blood to flow through the rest of the body

Schematic of the circulatory system showing typical pressures The two pumps in the heart increase pressure and that pressure is reduced as the blood flows through the body Long-term deviations from these pressures have medical implications discussed in some detail in the Fluid Dynamics and Its Biological and Medical Applications Only aortal or arterial blood pressure

can be measured noninvasively.

Pressure in the Eye

The shape of the eye is maintained by fluid pressure, called intraocular pressure, which

is normally in the range of 12.0 to 24.0 mm Hg When the circulation of fluid in the eye is blocked, it can lead to a buildup in pressure, a condition called glaucoma The net pressure can become as great as 85.0 mm Hg, an abnormally large pressure that can permanently damage the optic nerve To get an idea of the force involved, suppose the back of the eye has an area of 6.0 cm2, and the net pressure is 85.0 mm Hg Force is

given by F = PA To get F in newtons, we convert the area to m2 ( 1 m2= 104cm2) Then we calculate as follows:

F = hρgA =(85.0 × 10− 3m)(13.6 × 103kg/m3)(9.80 m/s2)(6.0 × 10− 4m2) = 6.8 N Eye Pressure

The shape of the eye is maintained by fluid pressure, called intraocular pressure When the circulation of fluid in the eye is blocked, it can lead to a buildup in pressure, a condition called glaucoma The force is calculated as

F = hρgA =(85.0 × 10− 3m)(13.6 × 103kg/m3)(9.80 m/s2)(6.0 × 10− 4m2) = 6.8 N

This force is the weight of about a 680-g mass A mass of 680 g resting on the eye (imagine 1.5 lb resting on your eye) would be sufficient to cause it damage (A normal force here would be the weight of about 120 g, less than one-quarter of our initial value.)

People over 40 years of age are at greatest risk of developing glaucoma and should have their intraocular pressure tested routinely Most measurements involve exerting a force

on the (anesthetized) eye over some area (a pressure) and observing the eye’s response

A noncontact approach uses a puff of air and a measurement is made of the force needed

to indent the eye ([link]) If the intraocular pressure is high, the eye will deform less and rebound more vigorously than normal Excessive intraocular pressures can be detected reliably and sometimes controlled effectively

The intraocular eye pressure can be read with a tonometer (credit: DevelopAll at the Wikipedia

Project.)

Calculating Gauge Pressure and Depth: Damage to the Eardrum

Suppose a 3.00-N force can rupture an eardrum (a) If the eardrum has an area of 1.00 cm2, calculate the maximum tolerable gauge pressure on the eardrum in newtons per meter squared and convert it to millimeters of mercury (b) At what depth in freshwater would this person’s eardrum rupture, assuming the gauge pressure in the middle ear is zero?

Strategy for (a)

The pressure can be found directly from its definition since we know the force and area

We are looking for the gauge pressure

Solution for (a)

Pg = F / A = 3.00 N / (1.00 × 10− 4m2) = 3.00 × 104N/m2

We now need to convert this to units of mm Hg:

Pg = 3.0 × 104N/m2(1.0 mm Hg

133 N/m2) = 226 mm Hg

Strategy for (b)

Here we will use the fact that the water pressure varies linearly with depth h below the

surface

Solution for (b)

P = hρg and therefore h = P / ρg Using the value above for P, we have

h = 3.0 × 104N/m2

(1.00 × 103kg/m3)(9.80 m/s2) = 3.06 m

Discussion

Similarly, increased pressure exerted upon the eardrum from the middle ear can arise when an infection causes a fluid buildup

Pressure Associated with the Lungs

The pressure inside the lungs increases and decreases with each breath The pressure drops to below atmospheric pressure (negative gauge pressure) when you inhale, causing air to flow into the lungs It increases above atmospheric pressure (positive gauge pressure) when you exhale, forcing air out

Lung pressure is controlled by several mechanisms Muscle action in the diaphragm and rib cage is necessary for inhalation; this muscle action increases the volume of the lungs thereby reducing the pressure within them[link] Surface tension in the alveoli creates a positive pressure opposing inhalation (SeeCohesion and Adhesion in Liquids: Surface Tension and Capillary Action.) You can exhale without muscle action by letting surface tension in the alveoli create its own positive pressure Muscle action can add to this positive pressure to produce forced exhalation, such as when you blow up a balloon, blow out a candle, or cough

The lungs, in fact, would collapse due to the surface tension in the alveoli, if they were not attached to the inside of the chest wall by liquid adhesion The gauge pressure in the liquid attaching the lungs to the inside of the chest wall is thus negative, ranging from − 4 to − 8 mm Hg during exhalation and inhalation, respectively If air is allowed

to enter the chest cavity, it breaks the attachment, and one or both lungs may collapse Suction is applied to the chest cavity of surgery patients and trauma victims to reestablish negative pressure and inflate the lungs

(a) During inhalation, muscles expand the chest, and the diaphragm moves downward, reducing pressure inside the lungs to less than atmospheric (negative gauge pressure) Pressure between the lungs and chest wall is even lower to overcome the positive pressure created by surface

tension in the lungs (b) During gentle exhalation, the muscles simply relax and surface tension

in the alveoli creates a positive pressure inside the lungs, forcing air out Pressure between the chest wall and lungs remains negative to keep them attached to the chest wall, but it is less

negative than during inhalation.

Other Pressures in the Body

Spinal Column and Skull

Normally, there is a 5- to12-mm Hg pressure in the fluid surrounding the brain and filling the spinal column This cerebrospinal fluid serves many purposes, one of which is

to supply flotation to the brain The buoyant force supplied by the fluid nearly equals the weight of the brain, since their densities are nearly equal If there is a loss of fluid, the brain rests on the inside of the skull, causing severe headaches, constricted blood flow, and serious damage Spinal fluid pressure is measured by means of a needle inserted between vertebrae that transmits the pressure to a suitable measuring device

Bladder Pressure

This bodily pressure is one of which we are often aware In fact, there is a relationship between our awareness of this pressure and a subsequent increase in it Bladder pressure climbs steadily from zero to about 25 mm Hg as the bladder fills to its normal capacity

of 500 cm3 This pressure triggers the micturition reflex, which stimulates the feeling of needing to urinate What is more, it also causes muscles around the bladder to contract, raising the pressure to over 100 mm Hg, accentuating the sensation Coughing, straining, tensing in cold weather, wearing tight clothes, and experiencing simple nervous tension all can increase bladder pressure and trigger this reflex So can the weight of a pregnant woman’s fetus, especially if it is kicking vigorously or pushing down with its head! Bladder pressure can be measured by a catheter or by inserting a needle through the bladder wall and transmitting the pressure to an appropriate measuring device One hazard of high bladder pressure (sometimes created by an obstruction), is that such pressure can force urine back into the kidneys, causing potentially severe damage

Pressures in the Skeletal System

These pressures are the largest in the body, due both to the high values of initial force, and the small areas to which this force is applied, such as in the joints For example, when a person lifts an object improperly, a force of 5000 N may be created between vertebrae in the spine, and this may be applied to an area as small as 10 cm2 The

pressure created is P = F / A = (5000 N) / (10− 3m2) = 5.0 × 106N/m2 or about 50 atm! This pressure can damage both the spinal discs (the cartilage between vertebrae), as well

as the bony vertebrae themselves Even under normal circumstances, forces between vertebrae in the spine are large enough to create pressures of several atmospheres Most

causes of excessive pressure in the skeletal system can be avoided by lifting properly and avoiding extreme physical activity (SeeForces and Torques in Muscles and Joints.)

There are many other interesting and medically significant pressures in the body For example, pressure caused by various muscle actions drives food and waste through the digestive system Stomach pressure behaves much like bladder pressure and is tied to the sensation of hunger Pressure in the relaxed esophagus is normally negative because pressure in the chest cavity is normally negative Positive pressure in the stomach may thus force acid into the esophagus, causing “heartburn.” Pressure in the middle ear can result in significant force on the eardrum if it differs greatly from atmospheric pressure, such as while scuba diving The decrease in external pressure is also noticeable during plane flights (due to a decrease in the weight of air above relative to that at the Earth’s surface) The Eustachian tubes connect the middle ear to the throat and allow us to equalize pressure in the middle ear to avoid an imbalance of force on the eardrum

Many pressures in the human body are associated with the flow of fluids Fluid flow will be discussed in detail in the Fluid Dynamics and Its Biological and Medical Applications

Section Summary

• Measuring blood pressure is among the most common of all medical

examinations

• The pressures in various parts of the body can be measured and often provide valuable medical indicators

• The shape of the eye is maintained by fluid pressure, called intraocular

pressure

• When the circulation of fluid in the eye is blocked, it can lead to a buildup in pressure, a condition called glaucoma

• Some of the other pressures in the body are spinal and skull pressures, bladder pressure, pressures in the skeletal system

Problems & Exercises

During forced exhalation, such as when blowing up a balloon, the diaphragm and chest muscles create a pressure of 60.0 mm Hg between the lungs and chest wall What force

in newtons does this pressure create on the 600 cm2surface area of the diaphragm?

479 N

You can chew through very tough objects with your incisors because they exert a large force on the small area of a pointed tooth What pressure in pascals can you create by exerting a force of 500 N with your tooth on an area of 1.00 mm2?

One way to force air into an unconscious person’s lungs is to squeeze on a balloon appropriately connected to the subject What force must you exert on the balloon with your hands to create a gauge pressure of 4.00 cm water, assuming you squeeze on an effective area of 50.0 cm2?

1.96 N

Heroes in movies hide beneath water and breathe through a hollow reed (villains never catch on to this trick) In practice, you cannot inhale in this manner if your lungs are more than 60.0 cm below the surface What is the maximum negative gauge pressure you can create in your lungs on dry land, assuming you can achieve − 3.00 cm water pressure with your lungs 60.0 cm below the surface?

−63.0 cm H2O

Gauge pressure in the fluid surrounding an infant’s brain may rise as high as 85.0 mm

Hg (5 to 12 mm Hg is normal), creating an outward force large enough to make the skull grow abnormally large (a) Calculate this outward force in newtons on each side of

an infant’s skull if the effective area of each side is 70.0 cm2 (b) What is the net force acting on the skull?

A full-term fetus typically has a mass of 3.50 kg (a) What pressure does the weight of such a fetus create if it rests on the mother’s bladder, supported on an area of 90.0 cm2

? (b) Convert this pressure to millimeters of mercury and determine if it alone is great enough to trigger the micturition reflex (it will add to any pressure already existing in the bladder)

(a) 3.81 × 103N/m2

(b) 28.7 mm Hg, which is sufficient to trigger micturition reflex

If the pressure in the esophagus is − 2.00 mm Hg while that in the stomach is +20.0 mm Hg, to what height could stomach fluid rise in the esophagus, assuming a density of 1.10 g/mL? (This movement will not occur if the muscle closing the lower end of the esophagus is working properly.)

Pressure in the spinal fluid is measured as shown in[link] If the pressure in the spinal fluid is 10.0 mm Hg: (a) What is the reading of the water manometer in cm water? (b) What is the reading if the person sits up, placing the top of the fluid 60 cm above the tap? The fluid density is 1.05 g/mL

A water manometer used to measure pressure in the spinal fluid The height of the fluid in the manometer is measured relative to the spinal column, and the manometer is open to the atmosphere The measured pressure will be considerably greater if the person sits up.

(a) 13.6 m water

(b) 76.5 cm water

Calculate the maximum force in newtons exerted by the blood on an aneurysm, or ballooning, in a major artery, given the maximum blood pressure for this person is 150

mm Hg and the effective area of the aneurysm is 20.0 cm2 Note that this force is great enough to cause further enlargement and subsequently greater force on the ever-thinner vessel wall

During heavy lifting, a disk between spinal vertebrae is subjected to a 5000-N compressional force (a) What pressure is created, assuming that the disk has a uniform circular cross section 2.00 cm in radius? (b) What deformation is produced if the disk is 0.800 cm thick and has a Young’s modulus of 1.5 × 109N/m2?

(a) 3.98 × 106Pa

(b) 2.1 × 10− 3cm

When a person sits erect, increasing the vertical position of their brain by 36.0 cm, the heart must continue to pump blood to the brain at the same rate (a) What is the gain

in gravitational potential energy for 100 mL of blood raised 36.0 cm? (b) What is the drop in pressure, neglecting any losses due to friction? (c) Discuss how the gain in gravitational potential energy and the decrease in pressure are related

(a) How high will water rise in a glass capillary tube with a 0.500-mm radius? (b) How much gravitational potential energy does the water gain? (c) Discuss possible sources of this energy

(a) 2.97 cm

(b) 3.39 × 10− 6J